Abstract: We report here on the discovery of stellar occultations, observed with
Kepler, that recur periodically at 15.685 hour intervals, but which vary in
depth from a maximum of 1.2% to a minimum that can be less than 0.2%. The star
that is apparently being occulted is KIC 12557548, a V = 16 magnitude K dwarf
with T_eff = 4400 K. The out-of-occultation behavior shows no evidence for
ellipsoidal light variations, indicating that the mass of the orbiting object
is less than ~3 M_J. Because the eclipse depths are highly variable, they
cannot be due solely to transits of a single planet with a fixed size. We
discuss but dismiss a scenario involving a binary giant planet whose mutual
orbit plane precesses, bringing one of the planets into and out of a grazing
transit. This scenario seems ruled out by the dynamical instability that would
result from such a configuration. The much more likely explanation involves
macroscopic particles - e.g., dust, possibly in the form of micron-sized
pyroxene grains - escaping the atmosphere of a slowly disintegrating planet not
much larger than Mercury in size. The planetary surface is hot enough to
sublimate; the resultant silicate vapor accelerates off the planet via a
Parker-type thermal wind, dragging dust grains with it. We infer a mass loss
rate from the observations of order ~1 M_earth/Gyr, with a dust-to-gas ratio
possibly of order unity. For our fiducial 0.1 M_earth planet (twice the mass of
Mercury), the evaporation timescale may be ~0.2 Gyr. Smaller mass planets are
disfavored because they evaporate still more quickly, as are larger mass
planets because they have surface gravities too strong to sustain outflows with
the requisite mass-loss rates. The occultation profile evinces an
ingress-egress asymmetry that could reflect a comet-like dust tail trailing the
planet; we present simulations of such a tail.